Neutron diffraction study of the atomic and molecular motion in hexamethylenetetramine

An accurate neutron diffraction study has been carried out on a single-crystal of hexamethylenetetramine and the measured Bragg intensities have been analysed for the effects of thermal motion. Four different models of the thermal motion have been used in a least-squares refinement of the data: (1) conventional model with ellipsoidal atomic probability density functions; (2) cumulant expansion model with the thermal motion of each atom represented by both second and third cumulant coefficients; (3) as model (1) but including the restriction imposed on the temperature factors by assuming rigid-body molecular motion; (4) as model (2) but including the rigid-body restriction. The best fit is given by model (2), which takes into account deviations from the ellipsoidal atomic probability density functions brought about by libration. Of the rigid-body models, refinement is better for (4) than for (3). Two parameters only, (u²) and (ω²) of paper I (Willis & Pawley, Acta Cryst. (1970), A26, 254) are needed to specify the atomic thermal motions for models (3) and (4), whereas nine parameters are required for model (1) and twenty for model (2). The lone-pair electrons of the nitrogen atom have been detected by combining, in a difference Fourier synthesis, the present data with the X-ray measurements of Becka & Cruickshank (Proc. Roy. Soc. A (1963), 273, 435).